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When Spain played Belgium in the preliminary round of the men's hockey competition in the 2008 Olympics, the final score was 4 - 2.
Can you find all the possible half time scores for this match?
This challenge invites pupils to develop a systematic way of working and offers the opportunity for discussion in pairs, small groups and the whole class. For some learners, having a 'real' context might provide motivation to solve the problem.
Of course, you may wish to introduce this problem in the context of the scores of a local event, rather than the Olympics. This may help many pupils engage in the solving of the problem.
You could ask "If there are $24$ possible different half time scores, what could the final score have been?".
Some pupils may prefer to start with games where there are fewer goals, for example, 0 - 1, 1 - 0, 1 - 1 etc so that there are fewer possible half time scores.